In this article, the interconnections between the ortho-positronium (the bound state of the positron and electron having parallel orientation of spills, (T)Ps) pick-off annihilation characteristics and concentration and effective size of elementary free volumes in polymer structures are discussed. Free volume parameters are responsible for many important properties of polymers Such as permeability to gases, selectivity, ageing mechanical strength, etc. However, the ways of quantitative estimations of size distributions of the free volume elements on the bases of experimental data are sometime not obvious. Various approaches to this problem are analyzed in this review mostly on examples of glassy polymer membrane materials. (C) 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2485-2503, 2008